m_white GeForce 2070 Ti SUPER paired with an Intel Core i7 10700k
N1X3L Could it be that the ISO is older than your hardware?
Solus Live/Installed both run fine on i7-10700 CPUs, which date to early 2020. The Nvidia GeForce 2070 Ti SUPER dates from 2019. So it isn't a case of new hardware. The issue is probably*** with the driver for the Nvidia GeForce 2070 Ti SUPER, as you correctly note.
Intel i7-10700 series CPUs (including the 10700K) have Intel UHD Graphics 630 onboard which also work fine on both Solus Live/Installed. Try removing the Nvidia GPU temporarily and installing Solus using the Intel onboard GPU. After Solus has installed, you should be able to install the appropriate Nvidia driver and then put the Nvidia GPU back into the computer.
I'm guessing that the right driver is the Linux X64 (AMD64/EM64T) Display Driver. I don't know if that driver is in the repository because I don't use that GPU.
I hope that someone will come along with better information about the correct driver.
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*** I assume, since you have Solus installed on your laptop, that you have BIOS set correctly for Solus on your desktop.